Dembele became the second-most expensive footballer in the world when he joined Barcelona from Borussia Dortmund in the summer, while Mbappe completed a loan move from Monaco to Paris Saint-Germain.
The pair are widely considered to be two of the best young talents in world football, but Neville has claimed that Rashford, who has five goals in eight United appearances this season, "is up there" with the French duo.
"Everybody praises Ousmane Dembele and Kylian Mbappe but nobody talks about Rashford in this country," Neville told Sky Sports News.
"Because he's English we just say 'he plays on the left wing, he's OK'. He is up there with Dembele and Mbappe, who also play on either wing. People say you have to play Rashford as a centre-forward but you can play him anywhere because he is good enough.
"Rashford is in the same bracket as those two - £100m-£150m players - he is every bit as good as those two and can be in the future because he is improving every season.
"He broke in under Louis van Gaal and set the world on fire, in his second season under Jose Mourinho everyone thought he wouldn't play but he did in all the big games. Now he is adding goals to his game and he can be absolutely world class."
Rashford scored twice as United booked their spot in the fourth round of the EFL Cup with a 4-1 win over Championship side Burton Albion on Wednesday night.